This means there are copyrights on the brand and on the product the flyer shows.

This is about patents (brevets d’invention), a trademark (marque) as well as models (modèles) for the product, which are registered (déposés ; there is plural agreement and all three components are registered). The past participle refers to a technical meaning of dépôt:

Dépôt d’une marque, d’un modèle, etc. Formalité administrative par laquelle un commerçant acquiert la propriété de sa création et la
protection de sa marque, de son modèle, etc. [TLFi]

In so many words that is an administrative formality, the filing of some document to some registrar to protect one’s work etc. An overview of some concepts of intellectual property/copyright in France may be useful; the patent, trademark and model can be registered individually, depending. For instance registering a drawing/model can grant product sale exclusivity in France for a term.

A flyer is usually localized and geared at a specific market, most likely France in this case. The content of a legal notice should not be tampered with to make it look casual, and one should ask the client for guidance here and seek professional advice and indeed not guess. On the other hand, the language is clear and there is no reference whatsoever to a patent pending nor to copyrights in what you presented.

Regardless of how (or even if) the referenced item (the official name of the product, for example) and the footnote itself are marked (with asterisks, numbers, “MD”s [or even with nothing at all]) in the original French flyer, I would mark them in the translated flyer with asterisks and include the following footnote text after the asterisk at the bottom:

• The [insert official name of product] is a protected trademark and
  is protected [internationally (if true)] by both design and utility
  patents. All rights reserved.

Personally, I would follow each instance of the product’s official name in the body of the flyer with an asterisk, but you’d probably be ok just using one/(or two) asterisk(s) in the body following either/(both) the product name’s first appearance or/(and) its most prominent appearance in the flyer.

You will note the use of “design [and utility] patents,” which is intended to capture the French notion of “modèles déposés,” and “… utility patents,” which is meant to cover “brevets [d’invention] déposés.”
(cf: Regarding a comment made elsewhere, while there is some similarity between and overlap of the protection afforded by “copyrights” and “design patents,” personally, I would not say that ‘copyright’ and ‘patent’ are synonyms in this or any other case.)

You will perhaps also note that “protected trademark,” instead of “registered trademark,” is used to attempt to capture “marque déposée.” I would avoid using “registered trademark” (and especially its abbreviated form/symbol “®”) anywhere on the flyer because of the [perhaps false] impression that its use could give concerning the product name’s official registration status with the US Patent and Trademark Office.

Notwithstanding any of the foregoing suggestions, I urge you to please heed the astute advice given elsewhere, which bears repeating here (with some emphasis and a parenthetical thought added):

A flyer is usually localized and geared at a specific market, most
likely France in this case. The content of a legal notice should not
be tampered with to make it look casual, and one should ask the client
for guidance here and seek professional advice and indeed [neither] guess (nor follow anonymous advice found on the Internet).

(+1, by the way, for having the admirable chutzpah to argue (successfully so far, and I hope it so remains) that your thought-provoking question involves “understanding French” and that it’s not purely a request for a translation!)